HGS MathComp Curriculum & Events

Objectives and goals:
To have a firm command of force-field-based methods in the modeling of molecular structures, dynamics and properties. Acquiring basic knowledge in MM, MD, MC and ligand-field-based modeling techniques. Advanced studies based on hands-on modeling, specifically also the application of the above techniques to solve the students own problems fundamental knowledge of chemistry and physics.

The covariance matrix and related
quantities, such as its inverse or its
principal components are fundamental
objects in the analysis of observed data. As
an example, Principal Component Analysis
is probably the most widely used statistical
technique for a variety of data analysis
tasks, including visualization, dimension
reduction, compression and regression.
Whereas originally both algorithms and
theory were developed for small to medium
sized datasets of relatively low dimension,
new applications involve the analysis of
massive and high dimensional datasets
whose covariance may be sparse, approxi-
mately low dimensional, or contain other
interesting structures. These settings
require new theory and algorithms for
successful data analysis.
Topics
Tuesday: The Sample and Population Covariance Matrices, Principal Component
Analysis (PCA), Singular Value Decomposition (SVD), Probabilistic
Formulations
Wednesday: Detection of Faint Signals and Dimensionality Reduction by PCA
Thursday, Friday: Covariance and PCA Estimation in High Dimensions and the
Role of Sparsity: Algorithms and Theory.

Network models are widely used to represent
relational information among interacting units
and the implications of these relations. This short
course is an overview of (social) network
modeling from the perspective of a statistician.
We will review the state of the art for networks
observed in cross-section or longitudinally. We
consider exponential-family and latent variable
models for networks. We also consider the
sampling of networks and inference based on
partially-observed networks. The course will
involve the practical application of the ideas and
their implementation through statistical software,
particularly the “statnet” open-source software
suite (http://statnet.org).
Mark S. Handcock is Professor of Statistics at the
University of California, Los Angeles. He has
published extensively on network modeling,
survey sampling, and network sampling
methods. His recent focus has been on the
development of statistical models for the analysis
of social network data, spatial processes and
demography

Topics
Basics Introduction, Graph Theory
Modeling Stochastic Models of Networks, Exponential-Family Random Graph Models
Inference Inference for Partially Observed Networks, Sampling of Networks (Design)
Analysis Network Dynamics
Practice statnet, an open-source software suite (http://statnet.org)

What is Software Engineering and how can it help me in developing better software? Software has become a solid part of research in many areas like physics, biology or medicine. It is used to simulate real world situations that are often too big or too small to be handled in any other way. Errors in Software can have an impact on research findings and at the end get very expensive to correct. Researchers developing software for their own use would like to spend less time coding and concentrate on their research instead. They want to be able to trust the results the software is delivering.
Software Engineering is a profession and field of study dedicated to designing, implementing, and modifying software so that it is of higher quality, more affordable, maintainable, and faster to build (wikipedia). In this course we will learn about some essential Software Engineering principles and techniques. We will take a look at the different activities in a software development process (e.g. design, implementation, testing). We will get to know the 10 software engineering practices (e.g. Version management, Issue Tracking) every scientific software project should use.
In the practical exercises we will take a look at some freeware tools available to accomplish the benefits we have learned about in the lectures.
In the fourth day of the compact you have the opportunity to try the introduced software engineering practices and tools on the software you are developing and discuss your specific software engineering problems with other course participants.
Link for more information and registration

Teilnehmer erhalten wichtige Informationen zu verschiedenen Übungen, damit ein bevorstehendes Assessment Center (AC) für sie bedenkenlos und erfolgreich verläuft. Teilnehmer trainieren unter anderem Selbstpräsentation, Gruppendiskussion und andere relevante Aufgaben aus Gruppenauswahlverfahren. Darüberhinaus erhalten die teilnehmer Informationen zu den Erwartungen der Personalverantwortlichen. Weiter lernen sie, worauf besonders geachtet wird und wie Bewerber auftreten sollen. Die teilnehmer erhalten ein validiertes Feedback zu ihren rethorischen Präsentationen anhand einer Videoanalyse.

Teilnehmer erhalten wichtige Informationen zu verschiedenen Übungen, damit ein bevorstehendes Assessment Center (AC) für sie bedenkenlos und erfolgreich verläuft. Teilnehmer trainieren unter anderem Selbstpräsentation, Gruppendiskussion und andere relevante Aufgaben aus Gruppenauswahlverfahren. Darüberhinaus erhalten die teilnehmer Informationen zu den Erwartungen der Personalverantwortlichen. Weiter lernen sie, worauf besonders geachtet wird und wie Bewerber auftreten sollen. Die teilnehmer erhalten ein validiertes Feedback zu ihren rethorischen Präsentationen anhand einer Videoanalyse.

Although the number of contacts and projects between the Republic of China and Germany is growing steadily, communication is not always that easy. Different ways of thinking and attitudes among team members quite often cause insecurity, irritations or misunderstanding because they are not familiar with the foreign culture. For Chinese students and employees in Germany, as well as for Germans in China, intercultural communication can be quite a challenge. This one-day workshop offers an important insight into Chinese culture, its impact on modern China and its way of life, and will also contrast similar situations in the German context.

- Do Germans organize everything around the dissertation like their Chinese counterparts, for example the accommodation?
- Are there specific ways of giving working instructions for a smooth functioning of the team?
- Differences in verbal and non-verbal communication
- How to keep your dissertation project running

Effective communication techniques, the Dos and Don’ts among Chinese and Germans will be discussed and worked out.
Dr. Hai Sun (bw-international) lives and works since 2000 in Germany. He is a long-standing trainer for intercultural communication and is also involved in Geman-Chinese projects.

3 hours lecture plus 1 hour practical

Acquire competence in analyzing optimization problems and designing and implementing solution algorithms by working on a specific optimization project including implementation of software, evaluation, documentation and public presentation of the results.

The course offers you programming skills and basic knowledge in combinatorial optimization

Learning the basics of generation and visualization of numerical solutions of (mainly optimization) problems with AG Bock software packages.

We consider a special class of multi-scale problems, concerning in particular thin composite reticulated structures (of lattice-type) which are periodic structures with big holes and a very small amount of material concentrated along layers (honeycomb struc- tures) or along bars (reinforced structures). They may have a very complex geometrical pattern. From the mathematical point of view, it means that we have to treat partial differential equations depending on several small parameters. The aim here is to give the asymptotic behavior of the solutions with respect to these parameters (which can be the period of the heterogeneities, the thickness of the material, or the thickness of a plate or of a beam in case respectively, of gridworks or cranes).
For the dependence on the period, we use homogenization methods (such as the periodic unfolding in perforated domains) in the directions in which we have periodicity. For the dependence on the small amount of material, a perturbation method is used, enabling us to give explicitly good approximations of real structures. The dependence on the third small parameter is studied by plate and beam techniques. We also give error estimates showing that the final result, when the small parameters are small enough, is close to the original physical one.
It is noteworthy that in all the cases we treat, we end up with simple partial differ- ential equations with constant coefficients that are explicit algebraic expressions of the physical ones.

The seminar focuses on current global and stochastic optimization research topics in nonlinear optimization. In particular, solutions for nonconvex problems and for optimization problems that involve uncertainty are highlighted. Knowledge of the lecture ,,Algorithmic Optimization´´ is recommended (or participation in the compact course ,,Nonlinear Optimization´´).

The seminar is suitable for HGS MathComp students.

FLUKA is a fully integrated particle physics Monte-Carlo simulation package. It has many applications in high energy experimental physics and engineering, shielding, detector and telescope design, cosmic ray studies, dosimetry, medical physics and radio-biology. More information, as well as related publications can be found on the FLUKA website. The course will help professionals working in the Monte Carlo radiation transport fields to understand the various functions and attributes of the code.
The event is organised with the support of the Interdisciplinary Center For Scientific Computing (IWR), the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences (HGS) and the Heidelberg Ion Beam Therapy Center (HIT), in particular of Dr. Michael Winckler (IWR/HGS) and PD. Dr. Katia Parodi (HIT).

The new journal Image Processing on Line http://www.ipol.im/
publishes image analysis algorithms. Each journal article has four parts:

a) a careful text description of the algorithm on the main web page;
b) an on line demo running the algorithm in real time;
c) a non-moderated archive of all experiments performed by users;
d) a commented code in C or C++.

According to the recent statistics of the first published articles, this
format permits a quick and strong diffusion.

The publication criterion is not the novelty, but the interest to the
scientific community of certifying and diffusing the algorithm. Each
submission is carefully evaluated to ensure "reproducible research". The
scientific editors request referees to check whether a), b), c) and d)
fit perfectly or not. Indeed, the main goal is to publish certified
reference versions of algorithms.

It is hoped that this new format will foster experiment sharing, on line
benchmarks, collaborative projects and in general accelerate research by
providing certified algorithms.

This journal is in the starting phase, but some fifteen algorithms are
in course of publication and twenty more submitted. A publication
on line is different from --and complementary to-- a journal
publication. I_ll describe briefly several on line algorithms, discuss
the technical and organization challenges of such publications, and take
all suggestions.

When building a mathematical model to describe the behavior of a physical system, one has often to face a certain level of uncertainty in the proper characterization of the model parameters and input data.

An example is given by the study of groundwater flow, where the subsurface permeability is largely unknown and often reconstructed from few available measurements via geostatistical techniques.

In this talk we focus on models based on Partial Differential Equations with random coefficients or forcing terms, where randomness is used to model our insufficient knowledge or intrinsic variability
of the physical system.

We first parametrize the random input data by a finite number or random variables. Then we approximate the functional dependence of the solution of the PDE on the random variables by global multivariate polynomials, exploiting the fact that such functional dependence is often highly smooth (even analytic).

We consider both Galerkin projection on polynomial spaces and Collocation type approximation on sparse grids of Gauss points. We focus, in particular, on the optimal choice of the polynomial space / sparse grid depending on the features of the differential problem at hand and the type of stochastic model for the coefficients. Our recipe for building the polynomial spaces based on a priori estimates is shown to be very effective on few numerical examples.

In this communication, we attempt to provide a self consistent picture, including existence
analysis and numerical solution algorithms, of the mathematical problems arising from
modeling photocurrent transients in Organic-polymer Solar Cells (OSCs). The mathemat-
ical model for OSCs consists of a system of nonlinear diffusion-reaction partial differential
equations (PDEs) with electrostatic convection, coupled to a ki- netic ordinary differen-
tial equation (ODE). We propose a suitable reformulation of the model that allows us to
prove the existence of a solution in both stationary and transient conditions and to bet-
ter highlight the role of exciton dynamics in determining the device turn-on time. For
the numerical treatment of the problem, we carry out a temporal semi-discretization using
an implicit adaptive method, and the resulting sequence of differential subproblems is lin-
earized using the Newton-Raphson method with inexact evaluation of the Jacobian. Then,
we use exponentially fitted finite elements for the spatial discretization, and we carry out
a thorough validation of the computational model by extensively investigating the impact
of the model parameters on photocurrent transient times. Finally we discuss the applica-
bility of the numerical algorithms developed for OSCs to the simulation of another classes
of advanced devices for solar energy conversion such as the dye-sensitized electrochemical
cells.
1. C. de Falco, R. Sacco, and M. Verri. Analytical and numerical study of photocurrent
transients in organic polymer solar cells. Comput. Methods Appl. Mech. Engrg.,
2010.

The humanoid robots are among the most complex robotic platforms and the most challenging to control. The main purpose of this lecture is to give
insights into the control of the humanoid robots and generating dynamically stable walking patterns.
To this end, a general introduction to robotics will be given at the beginning of the lecture and the application to the case of humanoid robots will be investigated afterward.

Keywords: Forward kinematics; Analytical and numerical inverse kinematics; Zero Moment Point; Walking patterns generation; Dynamics.

*The lecture will be given in English.

We discuss different time discretizations of variational type
applied to a nonlinear system of ordinary differential
equations which is generated by a semi-discretization in space
of a given nonlinear parabolic partial differential equation
like, for instance, the non-stationary Burgers equation.

Among these methods we compare the known continuous
Galerkin-Petrov and the discontinuous Galerkin method with
time polynomial ansatz functions of order k (cGP(k)- and
dG(k)-method) with respect to accuracy, stability and
computational costs. Moreover, we propose two new extended
methods (cGP-C1(k+1)- and dG-C0(k+1)-method) which have on the
one hand a one higher degree of ansatz functions and accuracy,
the same stability properties and on the other hand the same
computational costs as the original methods.

In literature various cost functions were proposed to explain observed
characteristics in human motions. The underlying assumption is that human
motions are (approximately) optimal with respect to the dynamics. Since
all of these cost functions seem to explain only a limited range of
motions, the question arises: Which cost function is the best for a
considered task? The application examples discussed in this talk are human
arm motions in two and three dimensions.

We use a bilevel optimization approach to solve the following inverse
problem: Which cost function out of a parametrized family composed from
functions suggested in literature reproduces recorded human motion best?
The lower level problem is an optimal control problem governed by a
nonlinear model of the human arm dynamics. The solution strategy is based
on a reformulation of the bilevel program as a one-level problem. This
problem is solved by an interior point solver and problem modifications to
increase solver performance are introduced; results of numerical tests will be stated.
In addition to the optimization results for experiments of human arm
motions, the transfer of obtained cost functions to robotic systems is
discussed.

Biped humanoid robot has a complex mechanical structure
composed of legs and upper body with arms, torso, and heads. Benefiting
from recent advancement of dynamic walking pattern generation,
whole-body motions have been studied more and more intensively in recent
humanoid research. In CNRS-AIST JRL (Joint Robotics Laboratory),
UMI3218/CRT, we have been working to improve the motion autonomy of the
robots by using the human-size humanoid robot platform HRP-2 that has
more than 30 degrees of freedom. In this talk, I present research
activities mainly conducted in the international joint laboratory
on whole-body humanoid motion planning and generation that integrate
biped locomotion, collision avoidance and manipulation.

The Distributed and Unified Numerics Environment (DUNE) is a software
framework for the numerical solution of partial differential equations
with grid-based methods. Using generic programming techniques it
strives for both: high flexibility (efficiency of the programmer) and
high performance (efficiency of the program). DUNE provides, among
other things, a large variety of local mesh refinement techniques, a
scalable parallel programming model, an ample collection of finite
element methods and efficient linear solvers.

This one week course will provide an introduction to the most
important DUNE modules. At the end the attendees will have a solid
knowledge of the simulation workflow from mesh generation and
implementation of finite element and finite volume methods to
visualization of the results. Successful participation requires
knowledge of object-oriented programming using C++ including generic
programming with templates (this knowledge will be brushed up on the
first day of the course). A solid background on numerical methods for
the solution of PDEs is expected.

Topics cover:

* Review of C++ programming techniques
* DUNE Grid interface
* Grid IO (pre- and postprocessing)
* DUNE PDELab
* Mesh Adaptivity
* Parallel computations
* Iterative Solvers
* Nonlinear problems
* Time-dependent problems